Epidemic transmission on SEIR stochastic models with nonlinear incidence rate

Our interest is to quantify the spread of an infective process with latency period and generic incidence rate that takes place in a Önite and homogeneous population. Within a stochastic framework, two random variables are deÖned to describe the variations of the number of secondary cases produced by an index case inside of a closed population. Computational algorithms are presented in order to characterize both random variables. Finally, theoretical and algorithmic results are illustrated by several numerical examples

Existence of periodic solutions for seasonal epidemic models with quarantine

In this work, we establish the existence of periodic orbits for a seasonal saturated epidemiological model of a population consisting of susceptible, infectious and quarantined individuals (an SIQS model). To do so, we use Leray-Schauder degree theory. We also provide numerical examples of these solutions

Modeling and analysis of SIR epidemic dynamics in immunization and cross-infection environments: Insights from a stochastic model

We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results

最終感染規模に対する隔離の効果に関する個体群動態モデル

Tohoku University博士（情報科学）thesi

Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence

In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts

Threshold dynamics of stochastic cholera epidemic model with direct transmission

This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition $\widetilde{R}_0$, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for $\widetilde{R}_0$, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection

Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources

A new network-based SIR epidemic model, which incorporates the individual medical resource factor and public medical resource factor is proposed. It is verified that the larger the public medical resource factor, the smaller the control reproduction number, and the larger individual medical resource factor can weaken the spread of diseases. We found that the control reproduction number below unity is not enough to ensure global asymptotic stability of the disease-free equilibrium. When the number of hospital beds or the individual medical resource factor is small enough, the system will undergoes backward bifurcation. Moreover, the existence and uniqueness of the optimal control and two time-varying variables’s optimal solutions are obtained. On the scale-free network, the level of optimal control is also proved to be different for different degrees. Finally, the theoretical results are illustrated by numerical simulations. This study suggests that maintaining sufficient both public medical resources and individual medical resources is crucial for the control of infectious diseases